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Kadison-Singer Conjecture Succumbs to Proof

Adam Marcus, Daniel A. Spielman—both of Yale University—and Nikhil Srivastava of Microsoft Research India have announced a proof of the Kadison-Singer conjecture.

The conjecture, formulated in 1959 by mathematicians Richard Kadison and Isadore Singer, has consequences for the foundations of physics.

To prove Kadison-Singer, Marcus, Spielman, and Srivastava applied a technique they developed—the 'method of interlacing families of polynomials'—to a statement known to imply it.

"My main reaction was awe at how beautiful the final proof was," Srivastava recalls. "I actually started laughing when I realized that it worked. It fit together so beautifully and sensibly you knew it was the 'right' proof and not something ad hoc."